Numerical Simulations of the 1-D Modified Burgers Equation

This paper shows the results yielded by several numerical methods when applied to the 1-D modified Burgers’ equation. In particular, the paper evaluates a new hybrid method against ten high-order methods when applied to the same equation. The novel numerical method for convection-dominated fluid or heat flows is based on the Hopmoc method and backward differentiation formulas. The results highlight that the new hybrid method yields promising accuracy results with regards to several existing high-order methods.